Rowley has rejected the allegations and said that he would work towards clearing his name.
Mr Rowley has also stepped down as deputy leader of the party, he said in a statement.
Scottish Labour will have a new leader on Saturday when the victor of the leadership race between Richard Leonard and Anas Sarwar will be announced.
The woman, has wished to remain anonymous, told the Scottish Sun the MSP "destroyed" her life after repeatedly sending her abusive text messages and stalking her, saying the abuse has left her "a shadow of the woman I once was".
Rowley denies the allegations and, in a statement, said: "I totally refute these allegations and will take all steps necessary to clear my name".
The interim leader of Scottish Labour has stepped aside, amid claims of misconduct.
"These allegations must be properly and thoroughly investigated in line with our party's procedures - and I will refer myself to the party so such an investigation can take place".
Mr Rowley, 53, was voted in as deputy Scottish Labour leader in August 2015.
Rowley, who took on the leadership post on an interim basis after the resignation of Kezia Dugdale in August, said the claims were baseless.
He was considered former prime minister Gordon Brown's right-hand man and protege after working as his assistant, election agent and constituency manager for five years.